optimal-ansatz-free-hamiltonian-learning

name	optimal-ansatz-free-hamiltonian-learning
description	Optimal ansatz-free Hamiltonian learning methodology — control-free, ancilla-free algorithm using randomized-sampling framework with band-limited kernel-based time sampling and displacement sieve for Hamiltonian structure learning. Use for quantum device calibration, signal sensing, and error correction.
metadata	{"arxiv_id":"2606.19486","published":"2026-06-17","authors":"Taiqi Zhou, Weiyuan Gong"}

Optimal Ansatz-free Hamiltonian Learning

Core Methodology

Randomized-Sampling Framework

• Learns ansatz-free Hamiltonian H with ||H|| ≤ Λ in total evolution time Θ(Λ/ε² log(Λ/ε))
• Proves matching lower bound Ω(Λ/ε² log(Λ/ε)) for any control-free protocol
• Uses only Pauli product state preparation and measurement — no ancilla, no interleaved control

Key Innovations

• Band-limited kernel-based time sampling: Characteristic probe time resolution depends only on Λ (not ε), making protocol practical for high-precision regimes
• Displacement sieve: Efficiently extracts Hamiltonian structure from sampled measurements
• Maintains optimal asymptotic cost under SPAM noise for local Hamiltonians

Comparison to Prior Work

Aspect	Prior Heisenberg-limited	This Work
Circuit depth	Deep circuits with interleaving probes	Control-free, ancilla-free
Time resolution	Extremely short (ε-dependent)	Λ-dependent only
State prep	Complex probe states	Pauli product states

Activation Keywords

• Hamiltonian learning, hamiltonian characterization
• Quantum device calibration, quantum sensing
• Ansatz-free learning, control-free learning
• 哈密顿量学习，量子设备标定

Usage Patterns

Pattern 1: Quantum Device Calibration

When calibrating unknown quantum hardware: use randomized-sampling framework instead of deep-circuit protocols for experimental feasibility.

Pattern 2: High-Precision Sensing

In high-precision regimes where ε << Λ: band-limited kernel sampling avoids the ε-dependent time resolution bottleneck.

Pattern 3: Local Hamiltonian Structure Learning

For systems known to be local: the displacement sieve efficiently extracts local interaction terms from Pauli measurements.

Pitfalls

• Lower bound applies only to control-free protocols — protocols with full control can potentially beat the bound
• SPAM noise robustness proven only for local Hamiltonians after calibration
• Total evolution time scales as Λ/ε² — becomes expensive for large Hamiltonian norms or very high precision